The invention relates to systems and techniques for mathematically modeling a human eye using topographical data measured from a human eye, using the mathematical model to simulate deformation of the eye by hypothetical incisions or excisions or ablations to arrive at an optimum surgical design by identifying the number, shape, location, length, and depth of the incisions or excisions or the shape, location, and quantity of corneal ablation(s). (It should be understood that hereinafter, including in the claims, the term "incision," which usually refers to a cut made by a scalpel, and the term "excision," which usually refers to a cut made by a laser beam, are considered to be interchangeable and to have the same meaning.)
Modern corneal refractive surgery originated with the work of Dr. Svyatoslav Fyodorov of Moscow and Dr. Jose Barraquer of Bogota, Columbia. Subsequently, various surgical techniques have been developed to alter the curvature of the cornea to correct refractive errors. The various techniques include incisional keratotomy using diamond blades, excisional keratotomy using laser beams to photo-disrupt molecules and ablate tissue in a linear pattern, ablative keratectomy or photo-refractive keratectomy using laser beams to remove larger areas of corneal tissue, mechanical removal and reshaping of corneal tissue (keratomileusis), and implantation of human or synthetic materials into the corneal stroma. All of the known procedures alter central corneal curvature by changing the structure of the cornea. All such refractive procedures are characterized by difficulty in predicting both the immediate and long term results, because of errors in calculations of pre-surgical measurements, failure to precisely implement the planned surgical techniques, and biological variances which affect immediate and long term results.
The cornea traditionally has been treated as a spherocylindrical lens, assuming that the radius of each individual meridian from the corneal apex to the corneal periphery is uniform. Prior methodologies tend to use an approximation to the topographic information of the cornea to determine the refractive power of the eye. In one known procedure, circular mires (reflected light images from the cornea conventionally used to mathematically calculate corneal curvature) are reflected from the corneal surface, and the difference between a given point on the mire and an adjacent mire is measured. A semi-quantitative estimate of the surface curvature is obtained by comparing this measurement with the values obtained using spheres of various radii. Prior mathematical models use a variety of approximations such as a simplified form of the corneal surface (e.g., spherical) or assume a symmetrical cornea (leading to a quarter model or an axisymmetric model) or use simplified material properties (e.g., isotropic), or assume small deformations or displacements, or do not consider clinically obtained data in the construction of the mathematical model.
Perhaps the closest prior art is indicated in the article "On the Computer-Aided and Optimal Design of Keratorefractive Surgery," by Steven A. Velinsky and Michael R. Bryant, published in Volume 8, page 173 of "Refractive and Corneal Surgery," March/April 1992. This article describes a computer-aided surgical design methodology, proposing that it could be an effective surgical design aid for the refractive surgeon, wherein the surgeon could choose constraints on surgical parameters such as minimum optical zone size, maximum depth of cut, etc., measure the patient's corneal topography, refractive error and possible other ocular parameters, and then review the computed results. The article refers to several mathematical models described in the literature, and how such mathematical models might be helpful. However, the article fails to disclose any particular adequate mathematical model of the cornea or any specific recommendation of surgical design that has been validated with clinical data.
The prior radial keratotomy procedures frequently result in large amounts of undercorrection or overcorrection. Prior keratotomy procedures often are based on experiential use of nomograms indicating appropriate surgical designs for a particular patient based on age, sex, refractive error, and intraocular pressure.
Finite element analysis is a known mathematically-based numerical tool that has been used to solve a variety of problems that are described by partial differential or integral equations. This technique has been used primarily in the area of solid mechanics, fluid mechanics, heat transfer, electromagnetics, acoustics, and biomechanics, including designing remedial techniques being developed for the human eye, to model internal structure and stresses in relation to various configurations of intraocular devices and corneal implants, as described in "Intraocular Lens Design With MSC/pal," by A. D. Franzone and V. M. Ghazarian in 1985 at the MSC/NASTRAN User's Conference in Pasadena, Calif., and in "Corneal Curvature Change Due to Structural Alternation by Radial Keratotomy," by Huang Bisarnsin, Schachar, and Black in Volume 110, pages 249-253, 1988 in the ASME Journal of Biomedical Engineering. Also see "Reduction of Corneal Astigmatism at Cataract Surgery," by Hall, Campion, Sorenson, and Monthofer, Volume 17, pages 407-414, July 1991 in the Journal of Cataract Refractive Surgery.
There clearly is an unmet need for an improved system for accurately predicting outcomes of hypothetical surgical procedures on the cornea to aid in the design of minimally invasive corneal surgery. There is an unmet need for a totally automated way of determining an optimal design of a surgical plan for incisional or excisional keratotomy or ablative keratectomy surgery to meet predetermined visual objectives with minimum invasiveness and minimum optical distortion. Further, it would be desirable to provide a technique for designing a multi-focal cornea that is similar to a gradient bifocal for patients that have presbyopia. It would be desirable to have an accurate mathematical model of the cornea for use in developing new surgical procedures without experimenting on live corneas.